Lévy processes and infinitely divisible distributions / Ken-iti Sato
Type de document : MonographieCollection : Cambridge studies in advanced mathematics, 68Langue : anglais.Pays: Grande Bretagne.Mention d'édition: reprintedÉditeur : Cambridge : Cambridge University Press, 2005Description : 1 vol. (XII-486 p.) ; 24 cmISBN: 0521553024.ISSN: 0950-6330.Bibliographie : Bibliogr. p. 451-478. Index.Sujet MSC : 60-02, Research exposition (monographs, survey articles) pertaining to probability theory60G51, Probability theory and stochastic processes, Processes with independent increments; Lévy processes
60G18, Probability theory and stochastic processes, Self-similar stochastic processesEn-ligne : Zentralblatt | MathSciNet
Item type | Current library | Call number | Status | Date due | Barcode |
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Monographie | CMI Salle 1 | 60 SAT (Browse shelf(Opens below)) | Available | 03897-01 |
Contient des exercices
Bibliogr. p. 451-478. Index
The first two chapters present basics: examples, connection between Lévy processes and infinitely divisible distributions. Chapter 3 treats the stable processes together with selfsimilar and selfdecomposable distributions. In Chapter 4 one finds the Lévy-Itô decomposition of sample functions of Lévy processes. Chapter 5 is devoted to properties of Lévy processes based on their distributions like moments, supports of the Lévy measures, continuity of the distributions. Subordination and time transformation is the topic of Chapter 6. In Chapter 7 the reader finds results on recurrence and transience of the underlying processes, and Chapter 8 contains the potential theory of Lévy processes, which is a generalization of the classical potential theory of the Laplacian, which is connected with the Brownian motion. Chapter 9 presents the Wiener-Hopf factorization and its consequences to short and long time behaviour of Lévy processes. The last Chapter 10 yields additional properties of infinitely divisible distributions.
Every chapter is finished by a series of ambitious exercises and notes, which include additional material, the solutions are given at the end of the book. The notes hint to further results in the literature and give insight into the history of the topics. More than five hundred references, all mentioned in the text, complete the survey on Lévy processes. (Zentralblatt)
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